This type of internal gear pump rotatably accommodates a ring-shaped internally toothed gear provided with internal teeth in a housing hole of a pump housing, and eccentrically accommodates inside the internally toothed gear an externally toothed gear provided with external teeth which internally mesh with the internal teeth of the internally toothed gear. The internally toothed gear is rotated by a rotational drive of the externally toothed gear. A liquid is sucked from a suction port, and is discharged from a discharge port through a maximum volume space defined by the external teeth and the internal teeth. In the external teeth of the externally toothed gears, a tooth bottom section is formed by a hypocycloid curve, a tooth tip section is formed by an epicycloid curve, and a meshing section between the tooth tip section and the tooth bottom section is formed by an involute curve. The internal tooth of the internally toothed gear is formed by an envelope of a tooth profile curve of the corresponding external tooth. Since the involute curve is not related to eccentricity between the externally toothed gear and the internally toothed gear, the eccentricity can be freely set. Thus, the eccentricity can be increased to achieve a large discharge amount. In addition, a clearance between the external teeth and the internal teeth can be minimized at a maximum volume space side and at a deepest meshing section side where the external tooth most deeply meshes with the internal tooth. Also, the clearance between the external tooth and the internal tooth can be increased at a suction port side and a discharge port side between the maximum volume space and the deepest meshing section. A contact between the external teeth and the internal teeth over the entire circumference is avoided to improve mechanical efficiency.